The Cure: Though I'm mixed about their music--some I like, some I loathe--their influence on alt/goth music is undeniable. Celebrating 30 years this year as an act that managed to take a seemingly niche musical form and make it palateable to a wide audience.
As frustrating a band as there is. They'll wow you with gorgeous pop hooks combined with strange arrangements - I'll bet "Just Like Heaven" is on more top 5 lists than any other song, the hit that never was- and then they'll do something so atrocious you think Robert Smith is a schizophrenic fraud.
I can't listen to "Boys Don't Cry" without thinking of Beat Night at Cooter's(?)
and falling in love over and over with that opening guitar line. "Friday I'm In Love" is the happiest tune ever written, so caught up with itself you want to bounce along with it even in the middle of a cheap department store when it comes over their sound system.
There's a lot of crap there, too, and maybe it's my obsession with melody and structure that makes me think that way, but I would vote them in based on their best work and their undeniable influence on music made 20 years later.